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Gabor Filter
In image processing, a Gabor filter, named after Dennis Gabor, who first proposed it as a 1D filter. The Gabor filter was first generalized to 2D by Gösta Granlund, by adding a reference direction. The Gabor filter is a linear filter used for texture analysis, which essentially means that it analyzes whether there is any specific frequency content in the image in specific directions in a localized region around the point or region of analysis. Frequency and orientation representations of Gabor filters are claimed by many contemporary vision scientists to be similar to those of the human visual system. They have been found to be particularly appropriate for texture representation and discrimination. In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by a sinusoidal plane wave (see Gabor transform). Some authors claim that simple cells in the visual cortex of mammalian brains can be modeled by Gabor functions. Thus, image analysis with Gabor filte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution Theorem
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms. Functions of a continuous variable Consider two functions u(x) and v(x) with Fourier transforms U and V: :\begin U(f) &\triangleq \mathcal\(f) = \int_^u(x) e^ \, dx, \quad f \in \mathbb\\ V(f) &\triangleq \mathcal\(f) = \int_^v(x) e^ \, dx, \quad f \in \mathbb \end where \mathcal denotes the Fourier transform operator. The transform may be normalized in other ways, in which case constant scaling factors (typically 2\pi or \sqrt) will appear in the convolution theorem below. The convolution of u and v is defined by: :r(x) = \(x) \triangleq \int_^ u(\tau) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bone
A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and enable mobility. Bones come in a variety of shapes and sizes and have complex internal and external structures. They are lightweight yet strong and hard and serve multiple functions. Bone tissue (osseous tissue), which is also called bone in the uncountable sense of that word, is hard tissue, a type of specialised connective tissue. It has a honeycomb-like matrix internally, which helps to give the bone rigidity. Bone tissue is made up of different types of bone cells. Osteoblasts and osteocytes are involved in the formation and mineralisation of bone; osteoclasts are involved in the resorption of bone tissue. Modified (flattened) osteoblasts become the lining cells that form a protective layer on the bone surface. The mine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trabecular
A trabecula (: trabeculae, from Latin for 'small beam') is a small, often microscopic, tissue element in the form of a small beam, strut or rod that supports or anchors a framework of parts within a body or organ. A trabecula generally has a mechanical function, and is usually composed of dense collagenous tissue (such as the trabecula of the spleen). It can be composed of other material such as muscle and bone. In the heart, muscles form trabeculae carneae and septomarginal trabeculae, and the left atrial appendage has a tubular trabeculated structure. Cancellous bone is formed from groupings of trabeculated bone tissue. In cross section, trabeculae of a cancellous bone can look like septa, but in three dimensions they are topologically distinct, with trabeculae being roughly rod or pillar-shaped and septa being sheet-like. When crossing fluid-filled spaces, trabeculae may offer the function of resisting tension (as in the penis, see for example trabeculae of corpora cav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feature Extraction
Feature may refer to: Computing * Feature recognition, could be a hole, pocket, or notch * Feature (computer vision), could be an edge, corner or blob * Feature (machine learning), in statistics: individual measurable properties of the phenomena being observed * Software feature, a distinguishing characteristic of a software program Science and analysis * Feature data, in geographic information systems, comprise information about an entity with a geographic location * Features, in audio signal processing, an aim to capture specific aspects of audio signals in a numeric way * Feature (archaeology), any dug, built, or dumped evidence of human activity Media * Feature film, a film with a running time long enough to be considered the principal or sole film to fill a program ** Feature length, the standardized length of such films * Feature story, a piece of non-fiction writing about news * Radio documentary (feature), a radio program devoted to covering a particular topic in so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gabor Function
In applied mathematics, Gabor atoms, or Gabor functions, are functions used in the analysis proposed by Dennis Gabor in 1946 in which a family of functions is built from translations and modulations of a generating function. Overview In 1946, Dennis Gabor Dennis Gabor ( ; ; 5 June 1900 – 9 February 1979) was a Hungarian-British physicist who received the Nobel Prize in Physics in 1971 for his invention of holography. He obtained British citizenship in 1946 and spent most of his life in Engla ... suggested the idea of using a granular system to produce sound. In his work, Gabor discussed the problems with Fourier analysis. Although he found the mathematics to be correct, it did not reflect the behaviour of sound in the world, because sounds, such as the sound of a siren, have variable frequencies over time. Another problem was the underlying supposition, as we use sine waves analysis, that the signal under concern has infinite duration even though sounds in real life have li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal
In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendicular'' is more specifically used for lines and planes that intersect to form a right angle, whereas ''orthogonal'' is used in generalizations, such as ''orthogonal vectors'' or ''orthogonal curves''. ''Orthogonality'' is also used with various meanings that are often weakly related or not related at all with the mathematical meanings. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics Optics In optics, polarization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Number
An imaginary number is the product of a real number and the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square (algebra), square of an imaginary number is . For example, is an imaginary number, and its square is . The number 0, zero is considered to be both real and imaginary. Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century). An imaginary number can be added to a real number to form a complex number of the form , where the real numbers and are called, respectively, the ''real part'' and the ''imaginary part'' of the complex number. History Although the Greek mathematician and engineer Heron of Alexandria is noted as the first t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
